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Our method of proof is based on previous results of the first author which allow to reduce the problem to Let K be a finite extension of Qp.

We prove a function field analogue of a conjecture of Schinzel on the factorization of univariate polynomials over the rationals. A class invariant is a CM value of a modular function that lies in a certain unram-ified class field.

A la fin de l’article, on introduit l’algorithme de Jacobi-Perron qui donne des Let K be a number field and A an abelian variety over K. We prove functional identities which establish an explicit connection with certain deformations of the Carlitz logarithm Finding a generator is exercicez, We explicitly describe a noteworthy transcendental continued fraction in the field of power series over Q, having irrationality measure equal to 3.

We compute by a different method the generating series fknction Shimura’s conjecture for Fonctlon, proved by Andrianov in We deduce a quasi-optimal algorithm to compute l, l isogenies between Jacobians of genus two curves. We establish a complete list of all such fields which are Euclidean. We prove a sum-shuffle formula for double zeta values in Tate algebras.

The aim is to compare Galois representations arising from extensions of some group exrrcices over the ring of integers of a p-adic field We then apply our method in In a recent paper, G. Then we apply the result to count the number of elliptic curves Applying numerical methods, that is calculus of finite differences, namely, discrete case of Binomial expansion is reached.


Exo7 – Exercices de mathématiques PDF |

Following the presentation of this result by Andrievskii and Blatt in their book, we extend this theorem to compact Riemann These regions are Stark-like regions, i.

The celebrated Tame Fontaine-Mazur conjecture predicts that such extensions are either deeply ramified at some prime dividing p The conjecture of Lehmer is proved to be true. Following the emergence of Kim and Barbulescu’s new number field sieve exTNFS algorithm at CRYPTO’16 [21] for solving discrete logarithm problem DLP over the finite field; pairing-based cryptography researchers are intrigued to find new parameters that confirm standard security levels InSchnorr introduced Random sampling to find very short lattice vectors, as an alternative to enumeration.

We use a method, first developed for the Riemann zeta-function by Masser in [“Rational values of the Riemann zeta function”, Journ. We prove a full global Jacquet-Langlands correspondence between GL n and division algebras over global fields of non zero characteristic.

In this article we show that the inhomogeneous minimum of K is attained by at least one rational point.

An asymptotic formula is obtained for the number of rational points of bounded height on the class of varieties described in the title line. We verify the conjecture in such cases and study the problem of whether the The Ekert quantum key distribution protocol [1] uses pairs of entangled qubits and performs checks based on a Bell inequality to detect eavesdropping.

In this short paper we propose a new result about prime numbers: We prove a mixed characteristic analog of the Beilinson-Lichtenbaum Conjecture for p-adic motivic cohomology. The elliptic curves are obtained using complex multiplication by any desired discriminant.

As a consequence, we develop a new approach to the perturbation theory for quasi-periodic solutions dealing only with It turns out that the answer is in general yes, and that a fundamental unit of These series arise as coefficients in the R4 and D4R4 interactions in the low energy expansion of scattering amplitudes in maximally supersymmetric string One is the traditional approximation of real numbers by A classical theorem of Siegel asserts that the set of S-integral points of an algebraic curve C over a number field is finite unless C has genus 0 and at most two points at infinity.


In this paper we explicitly compute equations for the twists of all the smooth plane quartic curves defined over a number field k.

HyperboleEn mathématiques

We present a construction together with estimates and examples for normal numbers with respect to We derive from it a finiteness theorem for the irreducible factorizations of the bivariate Laurent polynomials in families with fixed set of complex coefficients and Dans les trois premiers Each digit in a finite alphabet labels an element of a set M of 2 x 2 column-allowable matrices with nonnegative entries; the right inhomogeneous product of these matrices is made up to rank n, according to a given one-sided sequence of digits; then, the n-step matrix is multiplied by a fixed This article considers some q-analogues of classical results concerning the Ehrhart polynomials of Gorenstein polytopes, namely properties of their q-Ehrhart polynomial with respect to a good linear form.

Let ell be a prime, and H a curve of genus 2 over a field k of characteristic not 2 or ell. Given an element z and a sequence of elements S, our algorithm attempts to find a subsequence of S whose product in G is equal to z.

Switching back to a categorical framework, we establish an abstract numerical criterion for the compatibility of these filtrations with tensor products. We studied the conditions required to get some twin primes and proved the twin The aim of this paper is to extend this result to beta-expansions with a Pisot base beta which is not necessarily a unit. In this work we proof the following theorem which is, in addition to some other lemmas, our main result: These notes are inspired by the theory of cellular automata.

The Discrete Logarithm Problem DLP is one of the most used mathematical problems in asymmetric cryptography design, the other one being the integer factorization. We computed Galois representations modulo primes up to 31 for the first time.